Answered: Heights of men in America are usually a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Heights of men in America are usually a mean of 69.1 inches, with an SD of 2.67 inches. Women are also normally distributed, but with a mean of 64.2 inches instead and a standard deviation of 2.56 inches

If a male is 6 feet and 3 inches, what's his z-score?

If a woman is 5 feet and 11 inches, what's her z -score?

Who is the relatively taller one?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1:- Formula

Z score is given by,

Step 2:- Calculation

For male,

Given that, mean (mu) = 69.1

Standard deviation, sigma = 2.67

X= 6 feet 3 inches => 72 inches+3 inches = 75

Z = (75-69.1)/2.67

Z_male= 2.2097

For female,

Given that,

Mean (mu) = 64.2

Standard deviation, sigma= 2.56

X= 5 feet 11 inches = 60 inches+ 11 inches = 71 inches

Z score = (71-64.2)/2.56

Z_female= 2.656

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